We now extend our discussion towards a more complex, non-Markovian diffusion process, namely fractional Brownian motion (FBM).
Physically we could think, for example, of a colloidal particle diffusing through a homogeneous, yet viscoelastic medium (a situation which may be mapped onto FBM, see, e.g., [1]}). The homogeneity of the medium
allows one to consider the friction coefficient \(\gamma \) , and thus the mobility \(\mu =\gamma ^{-1}\) , as independent of space and time. The medium's viscoelasticity then enters only through the properties of the noise.
Specifically, we consider the LE
\(\dot{x}(t)= \mu F(x(t), \lambda (t))+ \xi ^H_{fGn}(t),\) 
